A186459 Number of (n+1) X 7 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

151, 197, 362, 673, 1061, 1693, 2377, 3677, 5073, 7977, 11533, 18221, 26957, 41729, 62105, 95205, 142645, 217581, 327233, 497481, 749885, 1137821, 1717565, 2603089, 3932825, 5956277, 9003685, 13630333, 20610673, 31193705, 47177837, 71391309

Offset

1,1

Comments

Column 6 of A186462.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>12.

Empirical g.f.: x*(151 - 105*x - 32*x^2 + 251*x^3 - 193*x^4 + 52*x^5 - 190*x^6 + 61*x^7 - 344*x^8 + 260*x^9 - 128*x^10 + 324*x^11) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018

Example

Some solutions for 3 X 7:
..1..1..0..0..0..0..1....0..1..0..1..0..0..0....1..1..1..1..1..1..1
..0..0..1..0..0..0..0....1..0..1..0..1..0..0....0..0..0..0..0..0..0
..0..0..0..1..0..0..0....0..1..0..1..0..1..1....0..0..0..0..0..0..0

Crossrefs

Cf. A186462.

Sequence in context: A139505 A095745 A112796 * A020359 A185936 A050969

Adjacent sequences: A186456 A186457 A186458 * A186460 A186461 A186462

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved